Classical automata capacity certificates factor through finite strong-power slices

Exact statement

If a classical graph-language $L\subseteq V(G)^*$ has growth $\rho$ , then every slice $L\cap V(G)^n$ is independent in $G^{\boxtimes n}$ , and for every $\varepsilon>0$ some finite slice has root rate above $\rho-\varepsilon$ . Reversible state splitting can compress or organize code families, but cannot yield a classical lower bound that does not factor through ordinary finite independent sets.

StatusDefinition-level proof; consistent with the primary regular-language capacity framework

External reviewMeiburg's regular-language framework is peer-reviewed; the FPRD methodological boundary has no documented specialist review.

Context

This closes an impossible win condition: any classical automaton accepting distinguishable words already emits conventional strong-power codes at every length.

Proof or evidence

Slice independence is the graph-language definition. The limsup defining growth supplies finite slices arbitrarily close to the automaton rate.

No-free-capacity boundary →

Verification notes

The boundary is symbolic; the two-block verifier supplies concrete reversible controls through three repeated blocks.

Limitations

The statement does not cover entanglement-assisted or other nonclassical channel models.
Automata may still offer exponential description compression and superior structured search.

Open work

Measure succinctness and verification cost separately from code size; call a capacity result new only when an emitted finite slice improves a published bound.